Thermodynamics

730 | ThermodynamicsMost air-conditioning processes can be modeled as steady-flow processes,and thus the mass balance relation ṁ in ṁ out can be expressed for dry airand water asMass balance for dry air: a m # a aoutm # a1kg>s2(14–16)inMass balance for water: a m # w aoutm # wor ainm # a v aoutm # a v (14–17)inDisregarding the kinetic and potential energy changes, the steady-flowenergy balance relation E . in E. out can be expressed in this case asQ # in W # in ainm # h Q # out W # out aoutm # h(14–18)The work term usually consists of the fan work input, which is small relativeto the other terms in the energy balance relation. Next we examinesome commonly encountered processes in air-conditioning.Heating coilsAir T 2T 1 , ω 1 , f 1 Heatω 2 = ω 1f 2 < f 1FIGURE 14–21During simple heating, specifichumidity remains constant, but relativehumidity decreases.v = constantCooling2f 2 = 80% f1 = 30%112°C 30°CFIGURE 14–22During simple cooling, specifichumidity remains constant, but relativehumidity increases.Simple Heating and Cooling (V constant)Many residential heating systems consist of a stove, a heat pump, or an electricresistance heater. The air in these systems is heated by circulating itthrough a duct that contains the tubing for the hot gases or the electric resistancewires, as shown in Fig. 14–21. The amount of moisture in the airremains constant during this process since no moisture is added to orremoved from the air. That is, the specific humidity of the air remains constant(v constant) during a heating (or cooling) process with no humidificationor dehumidification. Such a heating process proceeds in the directionof increasing dry-bulb temperature following a line of constant specifichumidity on the psychrometric chart, which appears as a horizontal line.Notice that the relative humidity of air decreases during a heating processeven if the specific humidity v remains constant. This is because the relativehumidity is the ratio of the moisture content to the moisture capacity of airat the same temperature, and moisture capacity increases with temperature.Therefore, the relative humidity of heated air may be well below comfortablelevels, causing dry skin, respiratory difficulties, and an increase instatic electricity.A cooling process at constant specific humidity is similar to the heatingprocess discussed above, except the dry-bulb temperature decreases and therelative humidity increases during such a process, as shown in Fig. 14–22.Cooling can be accomplished by passing the air over some coils throughwhich a refrigerant or chilled water flows.The conservation of mass equations for a heating or cooling process thatinvolves no humidification or dehumidification reduce to ṁ a1 ṁ a2 ṁa fordry air and v 1 v 2 for water. Neglecting any fan work that may be present,the conservation of energy equation in this case reduces toQ # m # a 1h 2 h 1 2orq h 2 h 1where h 1 and h 2 are enthalpies per unit mass of dry air at the inlet and theexit of the heating or cooling section, respectively.